5/4, 1 + square root of 3 write the polynomial function of least degree with integral coefficients that has the given zeros

Answer:

HUH

Step-by-step explanation:

According to the information

Andrew is increasing by a rate of 10%, whenever we are using the percentages it can be modeled using an exponential function

Sebastian on the other hand is increasing the same value each week, in this case it can be modeled using a linear function

Also by deffinition linear functions grow by equal differences and exponential functions grow by equal factors.

according to this the statements that are true are the third and forth statement

Answer:

4

Step-by-step explanation:

To find the unit rate you can pick any row and do y divided by x

For example, x = 3 and y = 12 so you can do 12 / 3 = 4.

You could also use x = 5 and y = 20, so it would be 20 / 5 = 5

Answer:

about 704 in 2

Step-by-step explanation:

surface area-2Ab+Pb*h

=2(13*8)+49.6(10)

=704

Answer:

10

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

f(-6)=5(3+6)+5    Distribute

f(-6)=15+30+5     Simplify

f(-6)=50               Write f value

f=50

Just took the test, so the answer is...

D. Horizontally compressed by a factor of 1/3

\(f(x)=\frac{1}{2}sin(x)-4\) is horizontally compressed by a factor of 1/3 to get \(f(x)=\frac{1}{2}sin(3x)-4\)

Option D is correct

Note that:

If a function \(f(x)=Asin(x)\) is transformed to \(g(x)=Asin(kx)\), it means that the function f(x) is horizontally compressed by 1/k

Relating this rule to the given function \(f(x)=\frac{1}{2}sin(x)-4\)

If x is replaced with 3x, the function will become:

\(f(x)=\frac{1}{2}sin(3x)-4\)

This means that the graph of  \(f(x)=\frac{1}{2}sin(x)-4\) is horizontally compressed by a factor of 1/3 to get \(f(x)=\frac{1}{2}sin(3x)-4\)

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Answer:

m∠WXZ = 38°

m∠ZXY = 52°

Step-by-step explanation:

In the question

∵ ∠WXY is a right angle

→ That means its measure is 90°

∴ m∠WXY = 90°

∵ m∠WXZ + m∠ZXY = m∠WXY

∵ m∠WXZ = (5x + 3)°

∵ m∠ZXY = (8x - 4)°

∵ m∠WXY = 90°

→ Substitute their values in the equation above

∴ (5x + 3) + (8x - 4) = 90

→ Add the like terms in the left side

∵ (5x + 8x) + (3 - 4) = 90

∴ 13x + (-1) = 90

∴ 13x - 1 = 90

→ Add 1 to both sides

∴ 13x - 1 + 1 = 90 + 1

∴ 13x = 91

→ Divide both sides by 13

∴ \(\frac{13x}{13}=\frac{91}{13}\)

∴ x = 7

→ To find the measure of each angle substitute x by 7 in their measures

∵ m∠WXZ = 5x + 3

∴ m∠WXZ = 5(7) + 3

∴ m∠WXZ = 35 + 3

∴ m∠WXZ = 38°

∵ m∠ZXY = 8x - 4

∴ m∠ZXY = 8(7) - 4

∴ m∠ZXY = 56 - 4

∴ m∠ZXY = 52°

The three accοmpanying questiοns, assuming that the firm is prοfit-maximizing and dοes nοt shut dοwn in the shοrt run

1)Firm's Tοtal Revenue=  $78000

2)Firm's Tοtal Cοst =$128700

3)Firm's Lοss = - $50700

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here in the given graph,

Cοst per unit = $300

Equilibrium quantity = $260 Then,

Firm's Tοtal Revenue = P * Q

=> $300*260 = $78000 (Equilibrium where, MR = MC)

Firm's Tοtal Cοst = Cοst per Unit * equilibrium quantity

=> $495*260 = $128,700

Firm's Lοss = TR - TC

=> $78000 - $128,700 = - $50700

Hence the answers are,

1)Firm's Tοtal Revenue=  $78000

2)Firm's Tοtal Cοst =$128700

3)Firm's Lοss = - $50700

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Answer: −5

Step-by-step explanation:

simplify: (−5)

Re-order terms so constants are on the left:

(−5)f(−5)−5

The number of words per second is 2/3 words per seconds.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Since there are 30 words in 45 seconds, the words per second will be:

= Number of words / Number of seconds

= 30/45

= 2/3

In conclusion, the words per second is 2/3.

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Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

Answer:

the answer is 4

Step-by-step explanation:

because there are 20 5's is 100 and 100 - 20 is 80 that eighty makes the five four.

To answer this question, we need to use scientific notation for the value of the radius as follows:

Then, using the formula for the area of a circle, we have:

Then, we have:

Therefore, the answer to this question is the first option: 4.59684 * 10^-5 pi square inches.

Answer:

B

Step-by-step explanation:

Function A: (4,0) and (2,10)

Slope: (10-0)/(2-4)

Slope: 10/-2 = -5

b = y - (m)(x)

b = 0 - (-5)(4)

b = 20

A. y = -5x + 20

A. y-intercept = 20

B. 2x - 2y = 30

2x - 30 = 2y

(2x - 30)/2 = y

x - 15 = y

y = X - 15

y-intercept = -15

Answer:

8 feet

Step-by-step explanation:

The diagram is attached below.

Note that the values are different but the diagram is similar. In this case,

Hypotenuse =17ft

Adjacent = 15²

Required

Opposite side

To get the feet of landscape edging would be required to outline the edge of the bed, we will use the Pythagoras theorem as shown;

Hyp² = Opp²+Adj²

Opp² = Hyp²-Adj²

l² = 17²-15²

l² = 289-225

l² = 64

l = √64

l = 8feet

Hence the feet of landscape edging would be required to outline the edge of the bed is 8 feet

Answer:01-80 + 15= |-65= -65 units

Step-by-step explanation:

Answer: 45

Step-by-step explanation:

The total profit in all was \(1040-900=\$ 140\).

The total profit per pizza was \((0.50)(8)=\$4\).

This means they sold \(\frac{140}{4}=35\) pizzas.

Adding this to the 10 pizzas held back, there were \(35+10=45\) pizzas in the original order.

Astronomers can use geometry to measure the distance of objects in space and describe ttheir relationship.

It should be noted that astronomers study stars, planets, and other celestial bodies. It should be noted that they use ground-based equipment, like optical telescopes, and space-based equipment. Some astronomers study distant galaxies and phenomena such as black holes and neutron stars.

In this case, astronomers can use geometry to measure the distance of objects in space and describe ttheir relationship.

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Answer:

distance between, motion

Step-by-step explanation:

plato, I got it right

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

The value of the expression is 9y⁵z³/x⁶

Note that index forms are described as mathematical forms of writing numbers that are large or too small in more convenient forms.

The rules of index forms are;

From the information given, we have that;

(y³z⁻¹) (3x⁻³y/z⁻²)²

expand the bracket, we get;

(y³z⁻¹) 9x⁻⁶y²/z⁻⁴

Take the inverse exponent of the denominator

(y³z⁻¹) 9x⁻⁶y²z⁴

Now, add the exponents

9x⁻⁶y³⁺²z⁻¹⁺⁴

9x⁻⁶y⁵z³

Then, we have;

9y⁵z³/x⁶

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The physical diameter of the sun will be 1309000km and the percentage of difference between the diameters will be 5.8%.

From the information, the sun has an angular diameter of about 0.5° and an average distance from the Earth of about 150 million km. The angular diameter in radians will be:

= 0.5π / 180

= 0.008727 radians

Distance from the sun = 150 × 10^6

The physical diameter of the sun will be:

= 150 × 10^6 × 0.008727

= 1309000km

The difference between the diameters will be:

= 1390000 - 1309000

= 8.1 × 10^4.

The percentage of difference will be:

= (8.1 * 10^4) / 1390000 × 100

= 5.8%

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

b

Step-by-step explanation:

Answer:

The answer is B! :)

Step-by-step explanation:

Answer:

fjvg8rg95ig9tjbopetjihefgiuo ugn idgjbiohionuion ijj ngibj irogjk0 krlkntirion pohtk ioh ht nh h h  h h h

Step-by-step explanation:

Answer:

6.1÷100×3200

press that you will get your answer

Answer:

538 books should be tested.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.99}{2} = 0.005\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.005 = 0.995\), so \(z = 2.575\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

How many books should be tested to estimate the average force required to break the binding to within 0.08 lb with 99% confidence?

n books should be tested.

n is found when \(M = 0.08\)

We have that \(\sigma = 0.72\)

\(M = z*\frac{\sigma}{\sqrt{n}}\)

\(0.08 = 2.575*\frac{0.72}{\sqrt{n}}\)

\(0.08\sqrt{n} = 2.575*0.72\)

\(\sqrt{n} = \frac{2.575*0.72}{0.08}\)

\((\sqrt{n})^{2} = (\frac{2.575*0.72}{0.08})^{2}\)

\(n = 537.1\)

Rounding up

538 books should be tested.

1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600